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A172358
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Triangle t(n,k) read by rows: Padovan factorial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized Padovan sequence with multiplier m=2.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 3, 9, 9, 3, 1, 1, 5, 15, 45, 15, 5, 1, 1, 9, 45, 135, 135, 45, 9, 1, 1, 11, 99, 495, 495, 495, 99, 11, 1, 1, 19, 209, 1881, 3135, 3135, 1881, 209, 19, 1, 1, 29, 551, 6061, 18183, 30305, 18183, 6061, 551, 29, 1
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OFFSET
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0,12
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COMMENTS
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Start from the generalized Padovan sequence A159284 and its partial products c(n) = 1, 1, 1, 1, 3, 9, 45, 405, 4455, 84645, 2454705... Then t(n,k) = c(n)/(c(k)*c(n-k)).
Row sums are 1, 2, 3, 4, 11, 26, 87, 380, 1707, 10490, 79955,...
Note that rows n>=14 contain fractions. R. J. Mathar, Jul 05 2012
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LINKS
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Table of n, a(n) for n=0..65.
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EXAMPLE
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1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 3, 3, 3, 1;
1, 3, 9, 9, 3, 1;
1, 5, 15, 45, 15, 5, 1;
1, 9, 45, 135, 135, 45, 9, 1;
1, 11, 99, 495, 495, 495, 99, 11, 1;
1, 19, 209, 1881, 3135, 3135, 1881, 209, 19, 1;
1, 29, 551, 6061, 18183, 30305, 18183, 6061, 551, 29, 1;
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MATHEMATICA
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Clear[f, c, a, t];
f[0, a_] := 0; f[1, a_] := 1; f[2, a_] := 1;
f[n_, a_] := f[n, a] = f[n - 2, a] + a*f[n - 3, a];
c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];
t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);
Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];
Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]
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CROSSREFS
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Sequence in context: A190906 A080311 A135368 * A119560 A172364 A140366
Adjacent sequences: A172355 A172356 A172357 * A172359 A172360 A172361
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KEYWORD
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nonn,tabl,less
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AUTHOR
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Roger L. Bagula, Feb 01 2010
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STATUS
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approved
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